I'm looking for the author and title of a book. I believe it's (supposed to be) the first in a trilogy, all using the same characters, but taking place in different universes - with only humans, with one type of aliens and with many aliens.

In it a gen-manipulated and very intelligent squid has been trained to fly a space-ship, and start exploring a planet and build a habitat. She (the squid) has managed to get pregnant, so by the time she dies, there are a whole colony of intelligent squids living in the habitat they've expanded.

Eventually there is a rift among the squids, and a group of them escapes in a space-ship they've built - just before the habitat is destroyed by the humans, because the squids threaten the mission.

I should point-out that most of the book was about the human characters, it's just that the squids were so special it stuck in my mind.

I may be mixing together with another book (but I don't think so), so here are few other things that (I think) happened:

Some sort of spreading cataclysmic event, that would swallow first the solar-system and eventually the whole galaxy/universe, setting a distinct time limit (very long time).

Some sort of portal that allowed travel into the very distant future - so distant actually, that one could observe the creation and destructions of several new universes, after first observing our own end. (I believe one of the squids was the first one through.)

2 Answers
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You're thinking of Manifold: Time (1999) by Stephen Baxter. It is the first book in the Manofold trilogy followed by Manifold: Space and Manifold: Origin.

Time is set on Earth, the inner part of the Solar System and various other universes onwards from the 21st century. The novel covers a wide range of topics, including the Doomsday argument, Fermi paradox, genetic engineering, and humanity's extinction.

The book begins at the end of space and time, when the last descendants of humanity face an infinite but pointless existence. Due to proton decay the physical universe has collapsed, but some form of intelligence has survived by embedding itself into a lossless computing substrate where it can theoretically survive indefinitely. However, because there will never be new input, eventually all possible thoughts will be exhausted. Some portion of this intelligence decides that this should not have been the ultimate fate of the universe, and takes action to change the past, centering on the early 21st century. The changes come in several forms, including a message to Reid Malenfant, the appearance of super-intelligent children around the world, and the discovery of a mysterious gateway on asteroid 3753 Cruithne.

Baxter's short story "Sheena 5" explores an alternate ending to the story of Sheena, the intelligent squid.

This theme first came up in Baxter's short story “Sheena 5”; see Variety SF for a review, which is much more about the squid and less about the humans.

But the really far fetched twist is - no humans will go there. A squid will have her mind genetically enhanced to make her smart, & to make her communicate with humans - particularly Dan! She will go in her tiny water habitat that will be part of the ship. No need to bother getting her back safely - since squids' natural life is only 2 years (I haven't verified it from other sources).

Sheena 5 is the squid that will go. Apparently, 5th in the line of engineered squid. Since she can never leave her water habitat, she will control an army of small robots that will actually do the construction job aboard the asteroid.

What no one foresaw was: she got pregnant just before the trip. Since she is smart, she gave birth in space in a way that hid the fact from mission control for too long. Now her craft is on asteroid, the rocket is fitted to asteroid & pushing it towards earth, but she has too many babies in her too small a habitat!

Turns out 4 of her babies are very smart; rest are typical dumb squids. Dumber ones will get eaten by their smarter siblings. But soon, the life support starts getting overstretched.

That is when Sheena 6, one of the smarter kids, makes Dan educate her on how to use local resources & her robots to extend the habitat. Expansion is done, & all is well for the moment.

Dan's lab is taken over by military, people lose interest in Project Bootstrap - the one that would have brought asteroid, Dan moves out. Years pass - less than a decade, I think.

Then, one fine day, someone manning Hubble II telescope decides to have a peek. And all hell breaks loose.

Not only have the squids made their little asteroid wholly habited, they have ships all over Sol! Reinmuth is headed to earth, & humans are afraid. Near end, we will see hints of the doom of humanity - as nuclear attack against Reinmuth fails, & it's entering earth's atmosphere. Sheena 46 appears to be in charge.

This answer was extensively edited yesterday by a moderator of this stack to add detailed spoilers (basically the entire plot of the story) which I would have never included. I'm not going to roll back a moderator's edits but I really resent having my name attached to what this answer has become.
– arpJan 15 at 0:44